Navier-Stokes bounds and scaling for compact trefoils in (2ℓπ)^3 domains

Over a wide range of viscosities, a perturbed trefoil vortex knot generates Reynolds number independent finite-time energy dissipation Δ E_ϵ (1) with evidence for a transient Kolmogorov spectra at the highest Reynolds number. Satisfying one definition for a dissipation anomaly. To cover the required range of Reynolds numbers, factors of ν^1/4 must be considered for both the largest scale L, the size of the periodic domain, which increases as L∼ν^-1/4, and vorticity moments at the the earliest times, which converge when scaled as ν^1/4Ω_m, including m=9,∞ at times t_∞<…更多